{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IBORGAROI5W2V4DPLWGYUWZWOF","short_pith_number":"pith:IBORGARO","canonical_record":{"source":{"id":"1908.03147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:19:23Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"f42aeb4e8be0bb07734349504ca05b01e0276c6d5d7c2fa580a6b8ea9ba363e4","abstract_canon_sha256":"612b5105856debcef4d751b4d9827cd3868507f5af1bf68efaf8e6d15134710d"},"schema_version":"1.0"},"canonical_sha256":"405d13022e476daaf06f5d8d8a5b36715bb40c4e9a30b83e0c45fd9a6f145cf1","source":{"kind":"arxiv","id":"1908.03147","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03147","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03147v2","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03147","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"IBORGAROI5W2","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_16","alias_value":"IBORGAROI5W2V4DP","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_8","alias_value":"IBORGARO","created_at":"2026-07-05T04:44:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IBORGAROI5W2V4DPLWGYUWZWOF","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:19:23Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"f42aeb4e8be0bb07734349504ca05b01e0276c6d5d7c2fa580a6b8ea9ba363e4","abstract_canon_sha256":"612b5105856debcef4d751b4d9827cd3868507f5af1bf68efaf8e6d15134710d"},"schema_version":"1.0"},"canonical_sha256":"405d13022e476daaf06f5d8d8a5b36715bb40c4e9a30b83e0c45fd9a6f145cf1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:17.488282Z","signature_b64":"9ioSD4MGbBhUjpeC+Ikl2yysRfiZvQRW1yZGDwm/A0CBOFuQPvLogkqWEjcYZIoEpnDTyU40JyiocesSpfpSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"405d13022e476daaf06f5d8d8a5b36715bb40c4e9a30b83e0c45fd9a6f145cf1","last_reissued_at":"2026-07-05T04:44:17.487886Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:17.487886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03147","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmf17HB9le1HwyRpAZvbtz1DjmSPfaFemHjUL0tIYB7uRn7akUnejq4dKbRNT+H9g3xnDOovRkd9QLQyCbNYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:39:12.301095Z"},"content_sha256":"32fb7c947222bea419169748f33fd88c856f14e1be99ec04b414379bb94a065c","schema_version":"1.0","event_id":"sha256:32fb7c947222bea419169748f33fd88c856f14e1be99ec04b414379bb94a065c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IBORGAROI5W2V4DPLWGYUWZWOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.AP","authors_text":"Carlo Orrieri, Matteo Muratori, Nicol\\`o De Ponti","submitted_at":"2019-08-08T16:19:23Z","abstract_excerpt":"Given a complete, connected Riemannian manifold $ \\mathbb{M}^n $ with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation with respect to the 2-Wasserstein distance. We produce (sharp) stability estimates under negative curvature bounds, which to some extent generalize well-known results by Sturm and Otto-Westdickenberg. The strategy of the proof mainly relies on a quantitative $L^1-L^\\infty$ smoothing property of the equation considered, combined with the Hamiltonian approach developed by Ambrosio, Mondino and Savar\\'e in a metric-mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03147","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03147/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioZyYLxC8+fDkJvy72cCAgTaZCBXO5egNwVGVVe1ZJHIZJ4bIv9NvcYvsWM2JfGWUo74+ki4bMBLpX6wZYIMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:39:12.301682Z"},"content_sha256":"6abbff2d0829792a48391348e22911210b6f7f0b196e1c61874d74f37abb565f","schema_version":"1.0","event_id":"sha256:6abbff2d0829792a48391348e22911210b6f7f0b196e1c61874d74f37abb565f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBORGAROI5W2V4DPLWGYUWZWOF/bundle.json","state_url":"https://pith.science/pith/IBORGAROI5W2V4DPLWGYUWZWOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBORGAROI5W2V4DPLWGYUWZWOF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T08:39:12Z","links":{"resolver":"https://pith.science/pith/IBORGAROI5W2V4DPLWGYUWZWOF","bundle":"https://pith.science/pith/IBORGAROI5W2V4DPLWGYUWZWOF/bundle.json","state":"https://pith.science/pith/IBORGAROI5W2V4DPLWGYUWZWOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBORGAROI5W2V4DPLWGYUWZWOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IBORGAROI5W2V4DPLWGYUWZWOF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"612b5105856debcef4d751b4d9827cd3868507f5af1bf68efaf8e6d15134710d","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:19:23Z","title_canon_sha256":"f42aeb4e8be0bb07734349504ca05b01e0276c6d5d7c2fa580a6b8ea9ba363e4"},"schema_version":"1.0","source":{"id":"1908.03147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03147","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03147v2","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03147","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"IBORGAROI5W2","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_16","alias_value":"IBORGAROI5W2V4DP","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_8","alias_value":"IBORGARO","created_at":"2026-07-05T04:44:17Z"}],"graph_snapshots":[{"event_id":"sha256:6abbff2d0829792a48391348e22911210b6f7f0b196e1c61874d74f37abb565f","target":"graph","created_at":"2026-07-05T04:44:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.03147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a complete, connected Riemannian manifold $ \\mathbb{M}^n $ with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation with respect to the 2-Wasserstein distance. We produce (sharp) stability estimates under negative curvature bounds, which to some extent generalize well-known results by Sturm and Otto-Westdickenberg. The strategy of the proof mainly relies on a quantitative $L^1-L^\\infty$ smoothing property of the equation considered, combined with the Hamiltonian approach developed by Ambrosio, Mondino and Savar\\'e in a metric-mea","authors_text":"Carlo Orrieri, Matteo Muratori, Nicol\\`o De Ponti","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:19:23Z","title":"Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03147","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:32fb7c947222bea419169748f33fd88c856f14e1be99ec04b414379bb94a065c","target":"record","created_at":"2026-07-05T04:44:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"612b5105856debcef4d751b4d9827cd3868507f5af1bf68efaf8e6d15134710d","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:19:23Z","title_canon_sha256":"f42aeb4e8be0bb07734349504ca05b01e0276c6d5d7c2fa580a6b8ea9ba363e4"},"schema_version":"1.0","source":{"id":"1908.03147","kind":"arxiv","version":2}},"canonical_sha256":"405d13022e476daaf06f5d8d8a5b36715bb40c4e9a30b83e0c45fd9a6f145cf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"405d13022e476daaf06f5d8d8a5b36715bb40c4e9a30b83e0c45fd9a6f145cf1","first_computed_at":"2026-07-05T04:44:17.487886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:17.487886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ioSD4MGbBhUjpeC+Ikl2yysRfiZvQRW1yZGDwm/A0CBOFuQPvLogkqWEjcYZIoEpnDTyU40JyiocesSpfpSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:17.488282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32fb7c947222bea419169748f33fd88c856f14e1be99ec04b414379bb94a065c","sha256:6abbff2d0829792a48391348e22911210b6f7f0b196e1c61874d74f37abb565f"],"state_sha256":"7e7454041e460137346583da7acb088ef84ca3dd0f823334b1c707ddbdaca992"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agrQrc7QRwvOXK+KfFjAvbEQS6rt5cmKYbG+t6/gbYYsou4AKIan5shU0ItIJ9+qjunYvtNLgNY/zr/Q0Aw/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:39:12.309049Z","bundle_sha256":"3fb9ebe8f8450b9afd57420b36b6bfb3b6d3e0c3ac1c2073474208d450736c6c"}}